Modeling of graded and multilayer ferroelectrics: Dielectric and piezoelectric response

Graded ferroelectrics and ferroelectric multilayers have received great interest as active elements in tunable microwave devices and piezoelectric actuators/sensors. There have been a number of experimental studies that show that these materials have many peculiar properties that cannot be described by a simple series connection of the individual layers that make up the heterostructures. A thermodynamic analysis is presented to demonstrate that ferroelectric multilayers interact through internal elastic, electrical, and electromechanical fields and the ??strength?? of the coupling can be quantitatively described using Landau theory of phase transformations, theory of elasticity, and principles of electrostatics. In addition to broken spatial inversion symmetry that can lead to asymmetric thermodynamic potentials, the modeling indicates that the electrostatic coupling between the layers leads to the suppression of ferroelectricity at a critical paraelectric layer thickness for ferroelectric-paraelectric bilayers. This bilayer is expected to have a colossal dielectric/piezoelectric response similar to the anomaly near Curie-Weiss temperature in homogeneous ferroelectrics at this critical thickness. This behavior has the characteristics of a ??phase transformation.?? The relative thicknesses of the layers can be used as a design parameter for bilayer, multilayers, and graded heterostructures. We present numerical results on the dielectric and piezoelectric response of BaTiO3/SrTiO3 bilayers, and graded BaTiO3-SrTiO3 (BST) and PbZrO3-PbTiO3 (PZT) compounds.